The subject invention relates generally to calorimeters and, more particularly, to thermoelectric calorimeters of the type in which heat flux is determined by an electrical signal induced by a temperature difference.
The transfer of thermal or heat energy is involved in many engineering design problems. A typical situation may extend from the design of a simple fluid heater to a complex heat transfer system for a re-entry vehicle.
In practice, heat transfer problems often prove too complicated to admit of a direct estimation of heat flow rates from temperature measurements and known thermal properties. Accordingly, there is a need for devices capable of direct measurement of heat fluxes. Although the rate of energy exchange of heat flux is a very fundamental parameter in any thermal analysis, it is not one that is readily measured, as in the case of temperature, for example.
Devices employed to measure thermal energy exchange are generally referred to as calorimeters. Through the years, many techniques have been employed to fabricate calorimeters for the purpose of measuring the rate of energy exchange between a given body and a source of heat. Generally, however, these techniques employ one of two fundamental concepts; thermal capacity, or thermal gradient.
In employing the concept of thermal capacity, the temperature rise of a known mass of a substance, such as water or a copper slug, is related to the rate of heat transfer to the substance. Devices employing this concept are, however, not readily applied to rapid transient measurements.
In employing the concept of thermal gradient, the rate of energy transfer to a substance, such as a solid, is related to a measurable temperature gradient on/or in the substance.
Several approaches have been taken in the development of calorimeters employing the concept of thermal gradient. In one category of devices the temperature difference over a finite thickness of material, so oriented that the heat will pass through the desired path to insure that the temperature difference measured will be proportional to the incident flux, is determined. In another series of devices temperatures histories at specific points within a solid are measured and the surface temperature gradient, and hence heat flux, may be analytically determined therefrom. However, the determination of heat flux based on temperature histories at specific points within a body has proven to be an exceedingly time consuming and expensive procedure and has only been resorted to in applications of an extremely unusual nature.
In certain process control applications, such as in the measure of heat flux losses from aluminum reduction cells, there exists a need for a rugged calorimeter that is able to withstand exceedingly high temperatures, rough handling, high humidity, and which is unaffected by aging and provides a reproducible thermal resistance and a reproducible heat flux calibration. In this regard, previous calorimeters or heat flow transducers of the thermal gradient variety have used plastic, ceramic, semi-conductor or metal thermal barriers in conjunction with various means for determining the temperature differential across these barriers to thereby determine heat flux therethrough. Unfortunately, plastics and semi-conductors do not stand up well under high temperatures; ceramics have proven brittle and readily damaged under any but the most careful handling; and metals provide too little temperature differential at relatively low heat flux.
A common problem in the design of any practical calorimeter is that the magnitude of response must be sufficient for measurement by available instrumentation. In considering the problem of designing a calorimeter of the thermal gradient type from the standpoint of response magnitude, one must envision a uniform heat flux .DELTA.F passing through a homogeneous infinite sheet of material having a thickness .delta. and a thermal conductivity k. Consider the flow of heat as perpendicular to the sheet and accompanied by temperature difference .DELTA.T between its two faces. Under steady-state conditions, it is known that .DELTA.F = k/.DELTA.T/.delta.. However, where .DELTA.T is small and is measured with a differential thermocouple system, it can be shown that .DELTA.T = .DELTA.e/c' , where .DELTA.e is the thermocouple EMF and c' is a temperature dependent coefficient computed from published tables for the particular thermocouple materials employed.
From the foregoing equations it follows that .DELTA.F = (k/c'.delta.).DELTA.e.
Clearly, if the values k, c', and .delta. are known, .DELTA.Fmay be readily calculated from .DELTA.e and the device can be used to measure heat fluxes and is therefore known as a calorimeter or heat meter.